The 27-year-old midfielder, who has spent nine years with the Robins after coming through their academy, is out of contract in the summer.
City's relegation from the Championship was confirmed last month, but O'Driscoll has said that he would like Skuse to remain at the club.
"He's available on a free transfer. I'd love him to stay, but that decision may have already been made," O'Driscoll told BBC Radio Bristol.
"He's a good lad and we've sat down and chatted about things."
Skuse has made 307 appearances for Bristol City, scoring nine goals.